CN116205863A - Method for detecting hyperspectral image abnormal target - Google Patents

Method for detecting hyperspectral image abnormal target Download PDF

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CN116205863A
CN116205863A CN202310108869.7A CN202310108869A CN116205863A CN 116205863 A CN116205863 A CN 116205863A CN 202310108869 A CN202310108869 A CN 202310108869A CN 116205863 A CN116205863 A CN 116205863A
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成宝芝
高艳
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Changzhou Institute of Technology
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Abstract

The invention relates to the technical field of detecting hyperspectral image abnormal targets, in particular to a method for detecting hyperspectral image abnormal targets, which aims at the problems that the existing hyperspectral image abnormal target detection technology still has complicated hyperspectral background information to limit the abnormal detection performance, the optimal rank is difficult to estimate, and the abnormal target detection efficiency is lower due to the limitation of image nonlinearity and Gao Weixing in the abnormal detection processing process, and the method comprises the following steps: s1: method combination, S2: obtaining an algorithm, S3: the invention aims to detect abnormal targets of a hyperspectral image by combining a representation-based method and a statistics-based method and utilizing the respective advantages of the method, inhibit partial background noise, improve the accuracy of detecting the abnormal targets of the hyperspectral image, and simultaneously ensure the stability and the accuracy of detection and improve the detection efficiency of the abnormal targets by using a k-means clustering method.

Description

Method for detecting hyperspectral image abnormal target
Technical Field
The invention relates to the technical field of detecting hyperspectral image abnormal targets, in particular to a method for detecting hyperspectral image abnormal targets.
Background
Hyperspectral images can more effectively identify and understand surface materials than multispectral images. Hyperspectral images are widely used in the fields of image quality assessment, image correction, classification, decomposition, target detection, and the like. Among them, because no prior information is required, hyperspectral anomaly target detection has been applied in many fields, such as: marine oil spill detection, battlefield target accurate identification, quality inspection of agricultural products and the like. In recent years, hyperspectral anomaly target detection has been studied in a large amount from the standpoint of algorithm implementation and application. In general, hyperspectral anomaly target detection algorithms can be divided into two categories: statistical-based methods and representation-based methods. The RX anomaly detection operator proposed by Reed and Xiaoli Yu is a classical method in a statistical-based anomaly detection algorithm. The method simplifies a background model of Gaussian multi-element distribution, and abnormal target detection is carried out by utilizing the Markov distance through the hyperspectral image characteristic that an abnormal target is different from background characteristic distribution. Due to the complexity of hyperspectral image distribution, background distribution often deviates from Gaussian distribution, so that the detection accuracy of the traditional RX anomaly detection operator method is low. The hyperspectral anomaly detection method based on representation mainly takes sparse representation, tensor decomposition and the like as core contents, and typical methods comprise a hyperspectral image anomaly target detection algorithm based on low-rank sparse matrix decomposition and the like. However, the existing representation-based method cannot solve the problems of background, abnormal targets, noise and the like well, and the effectiveness and the robustness of abnormal target detection are affected.
However, the existing technology for detecting the abnormal target of the hyperspectral image still has the problems that complicated hyperspectral background information limits the abnormal detection performance, the optimal rank is difficult to estimate, and the abnormal target detection efficiency is low due to the non-linearity of the image and the limitation of Gao Weixing in the abnormal detection processing process, so that a method for detecting the abnormal target of the hyperspectral image is provided for solving the problems.
Disclosure of Invention
The invention aims to solve the problems that the existing hyperspectral image abnormal target detection technology still has complicated hyperspectral background information to limit the abnormal detection performance, the optimal rank is difficult to estimate, the abnormal target detection efficiency is low due to the image nonlinearity and Gao Weixing limitation in the abnormal detection processing process, and the like.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method of detecting a hyperspectral image anomaly target, comprising the steps of:
s1: the method comprises the following steps: combining the representation-based method with the statistics-based method by a practitioner;
s2: the algorithm is obtained: obtaining a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation by a professional;
S3: the acquisition method comprises the following steps: acquiring an unsupervised learning method of K-means clustering by a professional;
s4: non-stationary signal processing: processing the non-stationary signal by a fractional Fourier transform method;
s5: and (3) constructing a model: constructing a low-rank sparse matrix decomposition model by professionals;
s6: algorithm optimization: optimizing a classical RX algorithm by a professional;
preferably, in the step S1, a professional combines a representation-based method and a statistics-based method, and detects an abnormal target through respective advantages of the methods, wherein the hyperspectral image is clustered into several subspaces by using a k-means clustering method, and the hyperspectral image is processed by using a fractional fourier transform and a low-rank and sparse matrix decomposition method, and simultaneously, the abnormal detection is performed in each subspace by using an improved RX detection method, and the detection result of each subspace is accumulated, and a final abnormal detection result is obtained through accumulation;
preferably, in the step S2, a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation is obtained by a professional, wherein the algorithm is input of original hyperspectral image data,
Figure BDA0004076031300000031
Initialization CL, num, pr, r, k,
Figure BDA0004076031300000032
Γ，W，S
the steps are as follows:
1) The original hyperspectral image Y passes through the formula (3) to obtain a clustering subspace
Figure BDA0004076031300000033
2) Obtained in each subspace by using a fractional Fourier transform algorithm
Figure BDA0004076031300000034
3) At the position of
Figure BDA0004076031300000035
In (2), { W) is obtained by using Godec algorithm 1 ,W 2 ,…W i ,…,W ε }
4)
Figure BDA0004076031300000036
5) In each subspace, an abnormality detection result { Θ ] is obtained by the equation (16) 1 ,Θ 2 ,…Θ i ,…Θ ε }
6) Finally, the final abnormality detection result is obtained
Figure BDA0004076031300000037
Outputting a hyperspectral image anomaly detection result graph;
preferably, in the step S3, a professional acquires an unsupervised learning method of K-means clustering, wherein the unsupervised learning method of K-means clustering is an iterative clustering algorithm and a data clustering technology, the data is divided into a specific number of clusters by the unsupervised learning method of K-means clustering, and the professional performs processing by the unsupervised learning method of K-means clustering, wherein the processing step is (a) a hypothetical hyperspectral image matrix when performing processing
Figure BDA0004076031300000041
Epsilon is the number of clusters, and the cluster center is assumed to be c= { C 1 ,c 2 ,c 3 ,…c j ,…c ε And Y is normalized, (B) randomly selecting B samples from the hyperspectral image dataset Y as initial cluster centers, (C) Y i (i=1, 2, … B; j=1, 2, … epsilon) is a sample in the hyperspectral image dataset and will be calculated from y i The distance to the cluster center is expressed as:
Figure BDA0004076031300000042
where L is the dimension of the sample, (D) find the minimum distance according to the calculated distance from each sample to the cluster center and divide the samples into corresponding clusters, (E) recalculate and update the cluster center according to equation (2) and calculate the result of the objective function according to equation (3) while judging the cluster center and the objective function, wherein the algorithm ends if the requirement is met and continues to step (B) if the requirement is not met, wherein the equation (2) is formulated as
Figure BDA0004076031300000043
(2) Equation (3) is
Figure BDA0004076031300000044
/>
Preferably, in the step S4, the non-stationary signal is processed by a fractional fourier transform method, wherein the processing is performed assuming a hyperspectral image matrix
Figure BDA0004076031300000045
N is the number of pixels, kappa is the number of spectral bands, described by the process, where for each pixel y i It is described in the fractional fourier transform domain using equations (4), (5) and (6), and the equation (4) is formulated as +.>
Figure BDA0004076031300000051
The formula of the equation (5) is +.>
Figure BDA0004076031300000052
The equation (6) is
Figure BDA00040760313000000510
Wherein->
Figure BDA0004076031300000053
And λ is an index, n is an integer, +.>
Figure BDA00040760313000000511
Is the fractional order of the fractional Fourier transform, and +.>
Figure BDA00040760313000000512
There is +.>
Figure BDA0004076031300000054
Figure BDA00040760313000000513
There is +.>
Figure BDA0004076031300000055
Said->
Figure BDA00040760313000000515
Is a rotation angle, and->
Figure BDA00040760313000000514
Preferably, in the step S5, a low-rank sparse matrix decomposition model is constructed by a professional, wherein the professional subjects the hyperspectral image matrix data in low-rank and sparse matrix decomposition
Figure BDA0004076031300000056
Modeling using equation (7), the equation (7) being y=w+s+e, where W represents the background of the hyperspectral image and is a low rank matrix, S represents the anomaly target in the hyperspectral image of the sparse matrix, E is the noise matrix in the hyperspectral image, and computing the low rank and sparse components using the GoDec algorithm by the constructed model, wherein equation (8) is used in the computation, the equation (8) being
Figure BDA0004076031300000057
Where r and k are the upper bound of the rank and radix S of matrix W, +.>
Figure BDA0004076031300000058
Is the Frobenius specification and optimizes the problem (8) by solving two sub-problems alternately using equation (9), where equation (9) is formulated as
Figure BDA0004076031300000059
And by singular values W t Threshold updating Y-S t-1 Wherein the singular value W t The calculation is performed using equation (10), wherein the equation (10) is expressed as +.>
Figure BDA0004076031300000061
svd(Y-S t-1 )＝UΛV T At the same time through the threshold Y-L of equation (11) t Updating S t Wherein the formula of the formula (11) is +.>
Figure BDA0004076031300000062
And Ω represents the first |Y-W t Non-zero subset k of i, and P Ω (. Cndot.) represents the projection of the matrix onto the set Ω, where the GoDec algorithm content is (a) input:. Cndot.,>
Figure BDA0004076031300000063
hyperspectral image data matrix
r- - -maximum rank of hyperspectral image background
k-hyperspectral image sparse matrix cardinality
Figure BDA0004076031300000064
Error tolerance
Γ - -maximum number of iterations
(b) Initialization r=r 0 ,k＝k 0 ,
Figure BDA0004076031300000065
Γ＝Γ 0 ，W 0 ＝Y，
S 0 ＝sparse(zeros(size(Y)))，t:＝0
(c) When (when)
Figure BDA0004076031300000066
Execution of
t:＝t+1
(d) Updating variable W t First, assume M 1 ＝randn(P,r),
T 1 ＝Y-S t-1 ，X 1 ＝T 1 M 1 ，
Figure BDA0004076031300000067
Ψ 1 ＝ZM 1 ，
M 2 ＝Ψ 1 ，Ψ 2 ＝Z T Ψ 1 ，Ψ 1 ＝ZΨ 2
If rank (M) 2 Ψ 1 )<r has
Figure BDA0004076031300000068
Returning to step (c); ending the program;
Figure BDA0004076031300000069
(e) Updating variable S t ,S t ＝P Ω (Y-W t )
(f) Output W, low rank component of hyperspectral image data
S, sparse component of hyperspectral image data, and obtaining RX detector method by improvement, wherein anomaly detection is performed by detecting result based on GoDec algorithm and processing low rank components W and S with RX detector, and in classical RX detectors 8,9, binary hypothesis of RX algorithm is defined as equation (12), equation (12) is that
Figure BDA0004076031300000071
Wherein H is 0 A=0, H when established 1 A > 0 when established, and B= [ B ] 1 ,b 2 ,…,b J ] T Light that is an abnormal targetSpectral features, β is the vector representing the background noise, and the two hypothesis tests have the same background covariance and different mean values, by assuming the target feature B and the background covariance + ->
Figure BDA0004076031300000072
Unknown, where H 0 Hyperspectral data are +.>
Figure BDA0004076031300000073
H 1 Hyperspectral data are +.>
Figure BDA0004076031300000074
RX applies a threshold to detect the Markov distance between the test pixel and its background, and assuming it satisfies the multivariate normal distribution 8, then equation (13) is obtained as
Figure BDA0004076031300000075
Wherein->
Figure BDA0004076031300000076
Is the background covariance matrix of the hyperspectral image data,/>
Figure BDA0004076031300000077
Is the sample mean of the hyperspectral image data, η is the threshold for abnormal target detection and the test allows a decision to be made between two hypothesis tests, where RX (Y) < η then H when a decision is made 0 Hold, and if there is no target hypothesis, H is the case when there is an abnormal target 1 The assumption is true;
preferably, in S6, the classical RX algorithm is optimized by a professional, wherein a low rank matrix w= { W is used first for the optimization 1 ,w 2 ,…,w N Building a background covariance matrix
Figure BDA0004076031300000078
The process employs equation (14) and equation (15), and the equation (14) is formulated as +.>
Figure BDA0004076031300000079
The formula of the equation (15) is +.>
Figure BDA00040760313000000710
Wherein N is the number of pixels, and equation (16) is obtained by calculation, wherein the equation (16) is expressed as +.>
Figure BDA00040760313000000711
And reconstructing the background in the anomaly detection by constructing a new background using the anomaly detection result of equation (16), selecting the first θ components, the background data to construct a covariance matrix by equations (14) and (15), and the anomaly detection to complete the anomaly detection result of obtaining a hyperspectral image by equation (16). />
Compared with the prior art, the invention has the beneficial effects that:
1. by combining the representation-based method and the statistics-based method, the abnormal target of the hyperspectral image is detected by utilizing the respective advantages of the method, partial background noise is restrained, and the detection precision of the abnormal target of the hyperspectral image is improved.
2. By using the k-means clustering method, the stability and accuracy of detection are ensured, and the detection efficiency of abnormal targets is improved.
The invention aims to detect abnormal targets of the hyperspectral image by combining a representation-based method and a statistics-based method and utilizing the respective advantages of the method, inhibit partial background noise, improve the accuracy of detecting the abnormal targets of the hyperspectral image, and simultaneously ensure the stability and the accuracy of detection and improve the detection efficiency of the abnormal targets by using a k-means clustering method.
Drawings
FIG. 1 is a flow chart of a method for detecting an abnormal object of a hyperspectral image according to the present invention;
FIG. 2 is a block diagram of an algorithm for detecting an abnormal target in a hyperspectral image according to the present invention
FIG. 3 is a graph of ROC curves of different methods for san_Diego dataset of a method for detecting a hyperspectral image anomaly target according to the present invention;
FIG. 4 is a ROC graph of different methods for detecting an abnormal target of a hyperspectral image according to the present invention in the abu-air-2 dataset;
FIG. 5 is a graph of ROC of different methods for detecting a hyperspectral image anomaly target in a HYDICE-uban dataset;
FIG. 6 is a graph of ROC curves of different methods for detecting Airport data sets of a method for detecting hyperspectral image anomaly targets according to the present invention;
FIG. 7 is a ROC graph of the Abu-uban-3 dataset of a method for detecting an outlier in a hyperspectral image according to the present invention.
Detailed Description
The following description of the technical solutions in the embodiments of the present invention will be clear and complete, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments.
Example 1
Referring to fig. 1-7, a method of detecting a hyperspectral image anomaly target includes the steps of:
s1: the method comprises the following steps: combining a representation-based method and a statistics-based method by professionals, and detecting an abnormal target through respective advantages of the methods, wherein a hyperspectral image is clustered into a plurality of subspaces by using a k-means clustering method, and the hyperspectral image is processed by using a fractional Fourier transform and a low-rank and sparse matrix decomposition method, and simultaneously, abnormality detection is performed in each subspace by using an improved RX detection method, detection results of each subspace are accumulated, and a final abnormality detection result is obtained through accumulation;
s2: the algorithm is obtained: obtaining a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation by a professional, wherein the algorithm is input by original hyperspectral image data,
Figure BDA0004076031300000091
Initialization CL, num, pr, r, k,
Figure BDA0004076031300000101
Γ，W，S
the steps are as follows:
1) The original hyperspectral image Y passes through the formula (3) to obtain a clustering subspace
Figure BDA0004076031300000102
2) Obtained in each subspace by using a fractional Fourier transform algorithm
Figure BDA0004076031300000103
3) At the position of
Figure BDA0004076031300000104
In (2), { W) is obtained by using Godec algorithm 1 ,W 2 ,…W i ,…,W ε }
4)
Figure BDA0004076031300000105
5) In each subspace, an abnormality detection result { Θ ] is obtained by the equation (16) 1 ,Θ 2 ,…Θ i ,…Θ ε }
6) Finally, the final abnormality detection result is obtained
Figure BDA0004076031300000106
Outputting a hyperspectral image anomaly detection result graph;
s3: the acquisition method comprises the following steps: an unsupervised learning method for obtaining K-means clustering by a professional, wherein the unsupervised learning method for K-means clustering is an iterative clustering algorithm and a data clustering technology, data is divided into a specific number of clusters by the unsupervised learning method for K-means clustering, and the processing is performed by the professional by the unsupervised learning method for K-means clustering, wherein the processing step is (a) a hypothetical hyperspectral image moment when the processing is performedArray
Figure BDA0004076031300000107
Epsilon is the number of clusters, and the cluster center is assumed to be c= { C 1 ,c 2 ,c 3 ,…c j ,…c ε And Y is normalized, (B) randomly selecting B samples from the hyperspectral image dataset Y as initial cluster centers, (C) Y i (i=1, 2, … B; j=1, 2, … epsilon) is a sample in the hyperspectral image dataset and will be calculated from y i The distance to the cluster center is expressed as:
Figure BDA0004076031300000111
where L is the dimension of the sample, (D) find the minimum distance according to the calculated distance from each sample to the cluster center and divide the samples into corresponding clusters, (E) recalculate and update the cluster center according to equation (2) and calculate the result of the objective function according to equation (3) while judging the cluster center and the objective function, wherein the algorithm ends if the requirement is met and continues to step (B) if the requirement is not met, wherein the equation (2) is formulated as
Figure BDA0004076031300000112
(2) Equation (3) is
Figure BDA0004076031300000113
S4: non-stationary signal processing: processing non-stationary signals by fractional Fourier transform, wherein the processing is performed assuming a hyperspectral image matrix
Figure BDA0004076031300000114
N is the number of pixels, kappa is the number of spectral bands, described by the process, where for each pixel y i It is described in the fractional fourier transform domain using equations (4), (5) and (6), and the equation (4) is formulated as +.>
Figure BDA0004076031300000115
The formula of the equation (5) is +.>
Figure BDA0004076031300000116
The formula of the equation (6) is +.>
Figure BDA0004076031300000117
Wherein->
Figure BDA0004076031300000118
And λ is an index, n is an integer, +.>
Figure BDA0004076031300000119
Is the fractional order of the fractional Fourier transform, and +.>
Figure BDA00040760313000001110
When there is
Figure BDA00040760313000001111
Figure BDA0004076031300000121
There is +.>
Figure BDA0004076031300000122
Said->
Figure BDA0004076031300000123
Is a rotation angle, and
Figure BDA0004076031300000124
s5: and (3) constructing a model: constructing a low-rank sparse matrix factorization model by a practitioner, wherein the practitioner matrix-data the hyperspectral image in the low-rank and sparse matrix factorization
Figure BDA0004076031300000125
Modeling is performed using equation (7), where equation (7) is given by y=w+s+e, where W represents the background of the hyperspectral image and is a low rank matrix, S tableShowing an abnormal target in the sparse matrix hyperspectral image, wherein E is a noise matrix in the hyperspectral image, and calculating low-rank and sparse components by using a GoDec algorithm through a constructed model, wherein the calculation is performed by using an equation (8), and the equation (8) is expressed as follows>
Figure BDA0004076031300000126
Where r and k are the upper bound of the rank and radix S of matrix W, +.>
Figure BDA0004076031300000127
Is the Frobenius specification and optimizes the problem (8) by solving two sub-problems alternately using equation (9), where equation (9) is formulated as +.>
Figure BDA0004076031300000128
And by singular values W t Threshold updating Y-S t-1 Wherein the singular value W t The calculation is performed by using the equation (10), wherein the equation (10) is as follows
Figure BDA0004076031300000129
svd(Y-S t-1 )＝UΛV T At the same time through the threshold Y-L of equation (11) t Updating S t Wherein the formula of the formula (11) is +.>
Figure BDA00040760313000001210
And Ω represents the first |Y-W t Non-zero subset k of i, and P Ω (. Cndot.) represents the projection of the matrix onto the set Ω, where the GoDec algorithm content is (a) input:. Cndot.,>
Figure BDA00040760313000001211
hyperspectral image data matrix
r- - -maximum rank of hyperspectral image background
k-hyperspectral image sparse matrix cardinality
Figure BDA0004076031300000131
Error tolerance
Γ - -maximum number of iterations
(b) Initialization r=r 0 ,k＝k 0 ,
Figure BDA0004076031300000132
Γ＝Γ 0 ，W 0 ＝Y，
S 0 ＝sparse(zeros(size(Y)))，t:＝0
(c) When (when)
Figure BDA0004076031300000133
Execution of
t:＝t+1
(d) Updating variable W t First, assume M 1 ＝randn(P,r),
T 1 ＝Y-S t-1 ，X 1 ＝T 1 M 1 ，
Figure BDA0004076031300000134
Ψ 1 ＝ZM 1 ，/>
M 2 ＝Ψ 1 ，Ψ 2 ＝Z T Ψ 1 ，Ψ 1 ＝ZΨ 2
If rank (M) 2 Ψ 1 )<r has
Figure BDA0004076031300000135
Returning to step (c); ending the program;
Figure BDA0004076031300000136
(e) Updating variable S t ,S t ＝P Ω (Y-W t )
(f) Output W, low rank component of hyperspectral image data
S, sparse components of the hyperspectral image data, and obtaining an RX detector method by modification, wherein anomaly detection is performed by a detection result based on a golec algorithm, and processing low rank components W and S with an RX detector, and in classical RX detectors 8,9,the binary hypothesis of the RX algorithm is defined as equation (12), which equation (12) is
Figure BDA0004076031300000137
Wherein H is 0 A=0, H when established 1 A > 0 when established, and B= [ B ] 1 ,b 2 ,…,b J ] T Is the spectral feature of the anomaly target, β is the vector representing the background noise, and the two hypothesis tests have the same background covariance and different mean values, by assuming the target feature B and the background covariance +.>
Figure BDA0004076031300000138
Unknown, where H 0 Hyperspectral data are +.>
Figure BDA0004076031300000141
H 1 Hyperspectral data are +.>
Figure BDA0004076031300000142
RX applies a threshold to detect the Markov distance between the test pixel and its background, and assuming it satisfies the multivariate normal distribution 8, then equation (13) is obtained as
Figure BDA0004076031300000143
Wherein->
Figure BDA0004076031300000144
Is the background covariance matrix of the hyperspectral image data,/>
Figure BDA0004076031300000145
Is the sample mean of the hyperspectral image data, η is the threshold for abnormal target detection and the test allows a decision to be made between two hypothesis tests, where RX (Y) < η then H when a decision is made 0 Hold, and if there is no target hypothesis, H is the case when there is an abnormal target 1 The assumption is true;
s6: algorithm optimization: the classical RX algorithm is optimized by the professional, wherein the optimization is performed by using low level firstRank matrix w= { W 1 ,w 2 ,…,w N Building a background covariance matrix
Figure BDA0004076031300000146
The process employs equation (14) and equation (15), and the equation (14) is formulated as +.>
Figure BDA0004076031300000147
The formula of the equation (15) is +.>
Figure BDA0004076031300000148
Wherein N is the number of pixels, and equation (16) is obtained by calculation, wherein the equation (16) is expressed as +.>
Figure BDA0004076031300000149
And reconstructing the background in the anomaly detection by constructing a new background using the anomaly detection result of equation (16), selecting the first θ components, the background data to construct a covariance matrix by equations (14) and (15), and the anomaly detection to complete the anomaly detection result of obtaining a hyperspectral image by equation (16).
Example two
Referring to fig. 1-7, a method of detecting a hyperspectral image anomaly target includes the steps of:
s1: the method comprises the following steps: combining the representation-based method and the statistics-based method by a practitioner, and detecting the abnormal target by respective advantages of the methods;
s2: the algorithm is obtained: obtaining a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation by a professional, wherein the algorithm is input by original hyperspectral image data,
Figure BDA0004076031300000151
Initialization CL, num, pr, r, k,
Figure BDA0004076031300000152
Γ，W，S
the steps are as follows:
1) The original hyperspectral image Y passes through the formula (3) to obtain a clustering subspace
Figure BDA0004076031300000153
2) Obtained in each subspace by using a fractional Fourier transform algorithm
Figure BDA0004076031300000154
3) At the position of
Figure BDA0004076031300000155
In (2), { W) is obtained by using Godec algorithm 1 ,W 2 ,…W i ,…,W ε }
4)
Figure BDA0004076031300000156
5) In each subspace, an abnormality detection result { Θ ] is obtained by the equation (16) 1 ,Θ 2 ,…Θ i ,…Θ ε }
6) Finally, the final abnormality detection result is obtained
Figure BDA0004076031300000157
Outputting a hyperspectral image anomaly detection result graph;
s3: the acquisition method comprises the following steps: an unsupervised learning method for obtaining K-means clustering by a professional, wherein the unsupervised learning method for K-means clustering is an iterative clustering algorithm and a data clustering technology, data is divided into a specific number of clusters by the unsupervised learning method for K-means clustering, and the processing is performed by the professional by the unsupervised learning method for K-means clustering, wherein the processing step is (a) a hypothetical hyperspectral image matrix when the processing is performed
Figure BDA0004076031300000158
Epsilon is the number of clusters, and the cluster center is assumed to be c= { C 1 ,c 2 ,c 3 ,…c j ,…c ε And Y is normalized, (B) randomly selecting B samples from the hyperspectral image dataset Y as initial cluster centers, (C) Y i (i=1, 2, … B; j=1, 2, … epsilon) is a sample in the hyperspectral image dataset and will be calculated from y i The distance to the cluster center is expressed as:
Figure BDA0004076031300000161
where L is the dimension of the sample, (D) find the minimum distance according to the calculated distance from each sample to the cluster center and divide the samples into corresponding clusters, (E) recalculate and update the cluster center according to equation (2) and calculate the result of the objective function according to equation (3) while judging the cluster center and the objective function, wherein the algorithm ends if the requirement is met and continues to step (B) if the requirement is not met, wherein the equation (2) is formulated as
Figure BDA0004076031300000162
(2) Equation (3) is
Figure BDA0004076031300000163
S4: non-stationary signal processing: processing non-stationary signals by fractional Fourier transform, wherein the processing is performed assuming a hyperspectral image matrix
Figure BDA0004076031300000164
N is the number of pixels, kappa is the number of spectral bands, described by the process, where for each pixel y i It is described in the fractional fourier transform domain using equations (4), (5) and (6), and the equation (4) is formulated as +.>
Figure BDA0004076031300000165
The formula of the equation (5) is +.>
Figure BDA0004076031300000171
The formula of the equation (6) is +.>
Figure BDA0004076031300000172
Wherein->
Figure BDA0004076031300000173
And λ is an index, n is an integer, +.>
Figure BDA0004076031300000174
Is the fractional order of the fractional Fourier transform, and +.>
Figure BDA0004076031300000175
When there is
Figure BDA0004076031300000176
Figure BDA0004076031300000177
There is +.>
Figure BDA0004076031300000178
Said->
Figure BDA0004076031300000179
Is a rotation angle, and
Figure BDA00040760313000001710
s5: and (3) constructing a model: constructing a low-rank sparse matrix factorization model by a practitioner, wherein the practitioner matrix-data the hyperspectral image in the low-rank and sparse matrix factorization
Figure BDA00040760313000001711
Modeling using equation (7), the equation (7) being y=w+s+e, where W represents the background of the hyperspectral image and is a low rank matrix, S represents the anomaly target in the hyperspectral image of the sparse matrix, E is the noise matrix in the hyperspectral image, and computing the low rank and sparse components using the GoDec algorithm by the constructed model, wherein the computation is performed using equation (8), whereThe equation (8) is given by +.>
Figure BDA00040760313000001712
Where r and k are the upper bound of the rank and radix S of matrix W, +.>
Figure BDA00040760313000001713
Is the Frobenius specification and optimizes the problem (8) by solving two sub-problems alternately using equation (9), where equation (9) is formulated as +.>
Figure BDA00040760313000001714
And by singular values W t Threshold updating Y-S t-1 Wherein the singular value W t The calculation is performed by using the equation (10), wherein the equation (10) is as follows
Figure BDA00040760313000001715
svd(Y-S t-1 )＝UΛV T At the same time through the threshold Y-L of equation (11) t Updating S t Wherein the formula of the formula (11) is +.>
Figure BDA0004076031300000181
And Ω represents the first |Y-W t Non-zero subset k of i, and P Ω (. Cndot.) represents the projection of the matrix onto the set Ω, where the GoDec algorithm content is (a) input:. Cndot.,>
Figure BDA0004076031300000182
hyperspectral image data matrix
r- - -maximum rank of hyperspectral image background
k-hyperspectral image sparse matrix cardinality
Figure BDA0004076031300000183
Error tolerance
Γ - -maximum number of iterations
(b) Initialization r=r 0 ,k＝k 0 ,
Figure BDA0004076031300000184
Γ＝Γ 0 ，W 0 ＝Y，
S 0 ＝sparse(zeros(size(Y)))，t:＝0
(c) When (when)
Figure BDA0004076031300000185
Execution of
t:＝t+1
(d) Updating variable W t First, assume M 1 ＝randn(P,r),
T 1 ＝Y-S t-1 ，X 1 ＝T 1 M 1 ，
Figure BDA0004076031300000186
Ψ 1 ＝ZM 1 ，
M 2 ＝Ψ 1 ，Ψ 2 ＝Z T Ψ 1 ，Ψ 1 ＝ZΨ 2
If rank (M) 2 Ψ 1 )<r has
Figure BDA0004076031300000187
Returning to step (c); ending the program;
Figure BDA0004076031300000188
(e) Updating variable S t ,S t ＝P Ω (Y-W t )
(f) Output W, low rank component of hyperspectral image data
S, sparse component of hyperspectral image data, and obtaining RX detector method by improvement, wherein anomaly detection is performed by detecting result based on GoDec algorithm and processing low rank components W and S with RX detector, and in classical RX detectors 8,9, binary hypothesis of RX algorithm is defined as equation (12), equation (12) is that
Figure BDA0004076031300000191
Wherein the method comprises the steps ofH 0 A=0, H when established 1 A > 0 when established, and B= [ B ] 1 ,b 2 ,…,b J ] T Is the spectral feature of the anomaly target, β is the vector representing the background noise, and the two hypothesis tests have the same background covariance and different mean values, by assuming the target feature B and the background covariance +.>
Figure BDA0004076031300000192
Unknown, where H 0 Hyperspectral data are +.>
Figure BDA0004076031300000193
H 1 Hyperspectral data are +.>
Figure BDA0004076031300000194
RX applies a threshold to detect the Markov distance between the test pixel and its background, and assuming it satisfies the multivariate normal distribution 8, then equation (13) is obtained as
Figure BDA0004076031300000195
Wherein->
Figure BDA0004076031300000196
Is the background covariance matrix of the hyperspectral image data,/>
Figure BDA0004076031300000197
Is the sample mean of the hyperspectral image data, η is the threshold for abnormal target detection and the test allows a decision to be made between two hypothesis tests, where RX (Y) < η then H when a decision is made 0 Hold, and if there is no target hypothesis, H is the case when there is an abnormal target 1 The assumption is true;
s6: algorithm optimization: the classical RX algorithm is optimized by the expert, wherein a low rank matrix w= { W is used first when the optimization is performed 1 ,w 2 ,…,w N Building a background covariance matrix
Figure BDA0004076031300000198
The process employs equation (14) and equation (15), and the equation (14) is formulated as +.>
Figure BDA0004076031300000199
The formula of the equation (15) is +.>
Figure BDA00040760313000001910
Wherein N is the number of pixels, and equation (16) is obtained by calculation, wherein the equation (16) is expressed as +.>
Figure BDA00040760313000001911
And reconstructing the background in the anomaly detection by constructing a new background using the anomaly detection result of equation (16), selecting the first θ components, the background data to construct a covariance matrix by equations (14) and (15), and the anomaly detection to complete the anomaly detection result of obtaining a hyperspectral image by equation (16).
Example III
Referring to fig. 1-7, a method of detecting a hyperspectral image anomaly target includes the steps of:
s1: the method comprises the following steps: combining a representation-based method and a statistics-based method by professionals, and detecting an abnormal target through respective advantages of the methods, wherein a hyperspectral image is clustered into a plurality of subspaces by using a k-means clustering method, and the hyperspectral image is processed by using a fractional Fourier transform and a low-rank and sparse matrix decomposition method, and simultaneously, abnormality detection is performed in each subspace by using an improved RX detection method, detection results of each subspace are accumulated, and a final abnormality detection result is obtained through accumulation;
S2: the algorithm is obtained: obtaining a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation by a professional;
s3: the acquisition method comprises the following steps: an unsupervised learning method for acquiring K-means clustering by professionals, wherein the unsupervised learning method for K-means clustering is an iterative clustering algorithm and a data clustering technology, and data are divided by the unsupervised learning method for K-means clusteringDividing into a specific number of clusters, and processing by a professional through an unsupervised learning method of the K-means clustering, wherein the processing step is (A) assumption of hyperspectral image matrix
Figure BDA0004076031300000201
Epsilon is the number of clusters, and the cluster center is assumed to be c= { C 1 ,c 2 ,c 3 ,…c j ,…c ε And Y is normalized, (B) randomly selecting B samples from the hyperspectral image dataset Y as initial cluster centers, (C) Y i (i=1, 2, … B; j=1, 2, … epsilon) is a sample in the hyperspectral image dataset and will be calculated from y i The distance to the cluster center is expressed as:
Figure BDA0004076031300000211
where L is the dimension of the sample, (D) find the minimum distance according to the calculated distance from each sample to the cluster center and divide the samples into corresponding clusters, (E) recalculate and update the cluster center according to equation (2) and calculate the result of the objective function according to equation (3) while judging the cluster center and the objective function, wherein the algorithm ends if the requirement is met and continues to step (B) if the requirement is not met, wherein the equation (2) is formulated as
Figure BDA0004076031300000212
(2) Equation (3) is
Figure BDA0004076031300000213
S4: non-stationary signal processing: processing non-stationary signals by fractional Fourier transform, wherein the processing is performed assuming a hyperspectral image matrix
Figure BDA0004076031300000214
N is the number of pixels, kappa is the number of spectral bands, described by the process, where for each pixel y i Which is in fractional order FourierThe Reed-Solomon transform domain is described using equations (4), (5) and (6), and the equation (4) is formulated as +.>
Figure BDA0004076031300000215
The formula of the equation (5) is +.>
Figure BDA0004076031300000216
The equation (6) is
Figure BDA0004076031300000217
Wherein->
Figure BDA0004076031300000218
And λ is an index, n is an integer, +.>
Figure BDA0004076031300000219
Is the fractional order of the fractional Fourier transform, and +.>
Figure BDA00040760313000002110
There is +.>
Figure BDA00040760313000002111
Figure BDA00040760313000002112
There is +.>
Figure BDA00040760313000002113
Said->
Figure BDA00040760313000002114
Is a rotation angle, and->
Figure BDA0004076031300000221
S5: and (3) constructing a model: constructing a low-rank sparse matrix factorization model by a practitioner, wherein the practitioner matrix-data the hyperspectral image in the low-rank and sparse matrix factorization
Figure BDA0004076031300000222
Modeling is performed by using equation (7), wherein the equation (7) is expressed as y=w+s+e, wherein W represents the background of the hyperspectral image and is a low-rank matrix, S represents an abnormal target in the hyperspectral image of the sparse matrix, E is a noise matrix in the hyperspectral image, and the low-rank and sparse components are calculated by using a GoDec algorithm through the constructed model, wherein the calculation is performed by using equation (8), and the equation (8) is expressed as >
Figure BDA0004076031300000223
Where r and k are the upper bound of the rank and radix S of matrix W, +.>
Figure BDA0004076031300000224
Is the Frobenius specification and optimizes the problem (8) by solving two sub-problems alternately using equation (9), where equation (9) is formulated as +.>
Figure BDA0004076031300000225
And by singular values W t Threshold updating Y-S t-1 Wherein the singular value W t The calculation is performed by using the equation (10), wherein the equation (10) is as follows
Figure BDA0004076031300000226
svd(Y-S t-1 )＝UΛV T At the same time through the threshold Y-L of equation (11) t Updating S t Wherein the formula of the formula (11) is +.>
Figure BDA0004076031300000227
And Ω represents the first |Y-W t Non-zero subset k of i, and P Ω (. Cndot.) represents the projection of the matrix onto the set Ω, where the GoDec algorithm content is (a) input:. Cndot.,>
Figure BDA0004076031300000228
hyperspectral image data matrix
r- - -maximum rank of hyperspectral image background
k-hyperspectral image sparse matrix cardinality
Figure BDA0004076031300000229
Error tolerance
Γ - -maximum number of iterations
(b) Initialization r=r 0 ,k＝k 0 ,
Figure BDA0004076031300000231
Γ＝Γ 0 ，W 0 ＝Y，
S 0 ＝sparse(zeros(size(Y)))，t:＝0
(c) When (when)
Figure BDA0004076031300000232
Execution of
t:＝t+1
(d) Updating variable W t First, assume M 1 ＝randn(P,r),
T 1 ＝Y-S t-1 ，X 1 ＝T 1 M 1 ，
Figure BDA0004076031300000233
Ψ 1 ＝ZM 1 ，
M 2 ＝Ψ 1 ，Ψ 2 ＝Z T Ψ 1 ，Ψ 1 ＝ZΨ 2
If rank (M) 2 Ψ 1 )<r has
Figure BDA0004076031300000234
Returning to step (c); ending the program;
Figure BDA0004076031300000235
(e) Updating variable S t ,S t ＝P Ω (Y-W t )
(f) Output W, low rank component of hyperspectral image data
S, sparse component of hyperspectral image dataAnd by improving the method of obtaining an RX detector in which anomaly detection is performed by detecting results based on the GoDec algorithm and processing low-rank components W and S with the RX detector, and in classical RX detectors 8,9, the binary hypothesis of the RX algorithm is defined as equation (12), said equation (12) being the equation
Figure BDA0004076031300000236
Wherein H is 0 A=0, H when established 1 A > 0 when established, and B= [ B ] 1 ,b 2 ,…,b J ] T Is the spectral feature of the anomaly target, β is the vector representing the background noise, and the two hypothesis tests have the same background covariance and different mean values, by assuming the target feature B and the background covariance +.>
Figure BDA0004076031300000237
Unknown, where H 0 Hyperspectral data are +.>
Figure BDA0004076031300000238
H 1 Hyperspectral data are +.>
Figure BDA0004076031300000239
RX applies a threshold to detect the Markov distance between the test pixel and its background, and assuming it satisfies the multivariate normal distribution 8, equation (13) is obtained as +.>
Figure BDA0004076031300000241
Wherein->
Figure BDA0004076031300000242
Is the background covariance matrix of the hyperspectral image data,/>
Figure BDA0004076031300000243
Is the sample mean of the hyperspectral image data, η is the threshold for abnormal target detection and the test allows a decision to be made between two hypothesis tests, where RX (Y) < η then H when a decision is made 0 Hold true and no target hypothesis existsH when abnormal target exists 1 The assumption is true;
s6: algorithm optimization: the classical RX algorithm is optimized by the expert, wherein a low rank matrix w= { W is used first when the optimization is performed 1 ,w 2 ,…,w N Building a background covariance matrix
Figure BDA0004076031300000244
The process employs equation (14) and equation (15), and the equation (14) is formulated as +.>
Figure BDA0004076031300000245
The formula of the equation (15) is +. >
Figure BDA0004076031300000246
Wherein N is the number of pixels, and equation (16) is obtained by calculation, wherein the equation (16) is expressed as +.>
Figure BDA0004076031300000247
And reconstructing the background in the anomaly detection by constructing a new background using the anomaly detection result of equation (16), selecting the first θ components, the background data to construct a covariance matrix by equations (14) and (15), and the anomaly detection to complete the anomaly detection result of obtaining a hyperspectral image by equation (16).
Example IV
Referring to fig. 1-7, a method of detecting a hyperspectral image anomaly target includes the steps of:
s1: the method comprises the following steps: combining a representation-based method and a statistics-based method by professionals, and detecting an abnormal target through respective advantages of the methods, wherein a hyperspectral image is clustered into a plurality of subspaces by using a k-means clustering method, and the hyperspectral image is processed by using a fractional Fourier transform and a low-rank and sparse matrix decomposition method, and simultaneously, abnormality detection is performed in each subspace by using an improved RX detection method, detection results of each subspace are accumulated, and a final abnormality detection result is obtained through accumulation;
s2: obtainingAlgorithm: obtaining a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation by a professional, wherein the algorithm is input by original hyperspectral image data,
Figure BDA0004076031300000251
Initialization CL, num, pr, r, k,
Figure BDA0004076031300000252
Γ，W，S
the steps are as follows:
1) The original hyperspectral image Y passes through the formula (3) to obtain a clustering subspace
Figure BDA0004076031300000253
2) Obtained in each subspace by using a fractional Fourier transform algorithm
Figure BDA0004076031300000254
3) At the position of
Figure BDA0004076031300000255
In (2), { W) is obtained by using Godec algorithm 1 ,W 2 ,…W i ,…,W ε }
4)
Figure BDA0004076031300000256
5) In each subspace, an abnormality detection result { Θ ] is obtained by the equation (16) 1 ,Θ 2 ,…Θ i ,…Θ ε }
6) Finally, the final abnormality detection result is obtained
Figure BDA0004076031300000257
Outputting a hyperspectral image anomaly detection result graph;
s3: the acquisition method comprises the following steps: unsupervised learning method for obtaining K-means clustering by professionals, wherein the K-means clusteringThe non-supervision learning method of class is an iterative clustering algorithm and a data clustering technology, the data is divided into a specific number of clusters by the non-supervision learning method of K-means clustering, and the processing is carried out by professionals by the non-supervision learning method of K-means clustering, wherein the processing steps are (A) the hypothesized hyperspectral image matrix when the processing is carried out
Figure BDA0004076031300000261
Epsilon is the number of clusters, and the cluster center is assumed to be c= { C 1 ,c 2 ,c 3 ,…c j ,…c ε And Y is normalized, (B) randomly selecting B samples from the hyperspectral image dataset Y as initial cluster centers, (C) Y i (i=1, 2, … B; j=1, 2, … epsilon) is a sample in the hyperspectral image dataset and will be calculated from y i The distance to the cluster center is expressed as:
Figure BDA0004076031300000262
where L is the dimension of the sample, (D) find the minimum distance according to the calculated distance from each sample to the cluster center and divide the samples into corresponding clusters, (E) recalculate and update the cluster center according to equation (2) and calculate the result of the objective function according to equation (3) while judging the cluster center and the objective function, wherein the algorithm ends if the requirement is met and continues to step (B) if the requirement is not met, wherein the equation (2) is formulated as
Figure BDA0004076031300000263
(2) Equation (3) is
Figure BDA0004076031300000264
S4: and (3) constructing a model: constructing a low-rank sparse matrix factorization model by a practitioner, wherein the practitioner matrix-data the hyperspectral image in the low-rank and sparse matrix factorization
Figure BDA0004076031300000265
Modeling using equation (7), the equation (7) being y=w+s+e, where W represents the background of the hyperspectral image and is a low rank matrix, S represents the anomaly target in the hyperspectral image of the sparse matrix, E is the noise matrix in the hyperspectral image, and computing the low rank and sparse components using the GoDec algorithm by the constructed model, wherein equation (8) is used in the computation, the equation (8) being
Figure BDA0004076031300000271
Where r and k are the upper bound of the rank and radix S of matrix W, +. >
Figure BDA0004076031300000272
Is the Frobenius specification and optimizes the problem (8) by solving two sub-problems alternately using equation (9), where equation (9) is formulated as
Figure BDA0004076031300000273
And by singular values W t Threshold updating Y-S t-1 Wherein the singular value W t The calculation is performed using equation (10), wherein the equation (10) is expressed as +.>
Figure BDA0004076031300000274
svd(Y-S t-1 )＝UΛV T At the same time through the threshold Y-L of equation (11) t Updating S t Wherein the formula of the formula (11) is +.>
Figure BDA0004076031300000275
And Ω represents the first |Y-W t Non-zero subset k of i, and P Ω (. Cndot.) represents the projection of the matrix onto the set Ω, where the GoDec algorithm content is (a) input:. Cndot.,>
Figure BDA0004076031300000276
hyperspectral image data matrix
r- - -maximum rank of hyperspectral image background
k-hyperspectral image sparse matrix cardinality
Figure BDA0004076031300000277
Error tolerance
Γ - -maximum number of iterations
(b) Initialization r=r 0 ,k＝k 0 ,
Figure BDA0004076031300000278
Γ＝Γ 0 ，W 0 ＝Y，
S 0 ＝sparse(zeros(size(Y)))，t:＝0
(c) When (when)
Figure BDA0004076031300000279
Execution of
t:＝t+1
(d) Updating variable W t First, assume M 1 ＝randn(P,r),
T 1 ＝Y-S t-1 ，X 1 ＝T 1 M 1 ，
Figure BDA0004076031300000281
Ψ 1 ＝ZM 1 ，
M 2 ＝Ψ 1 ，Ψ 2 ＝Z T Ψ 1 ，Ψ 1 ＝ZΨ 2
If rank (M) 2 Ψ 1 )<r has
Figure BDA0004076031300000282
Returning to step (c); ending the program;
Figure BDA0004076031300000283
(e) Updating variable S t ,S t ＝P Ω (Y-W t )
(f) Output W, low rank component of hyperspectral image data
S, sparse component of hyperspectral image data, and by improvementAn RX detector method is obtained wherein anomaly detection is performed by a detection result based on the GoDec algorithm and processing low rank components W and S with an RX detector, and in classical RX detectors 8,9, the binary hypothesis of the RX algorithm is defined as equation (12), said equation (12) being
Figure BDA0004076031300000284
Wherein H is 0 A=0, H when established 1 A > 0 when established, and B= [ B ] 1 ,b 2 ,…,b J ] T Is the spectral feature of the anomaly target, β is the vector representing the background noise, and the two hypothesis tests have the same background covariance and different mean values, by assuming the target feature B and the background covariance +.>
Figure BDA0004076031300000285
Unknown, where H 0 Hyperspectral data are +.>
Figure BDA0004076031300000286
H 1 Hyperspectral data are +.>
Figure BDA0004076031300000287
RX applies a threshold to detect the Markov distance between the test pixel and its background, and assuming it satisfies the multivariate normal distribution 8, then equation (13) is obtained as
Figure BDA0004076031300000288
Wherein->
Figure BDA0004076031300000289
Is the background covariance matrix of the hyperspectral image data,/>
Figure BDA00040760313000002810
Is the sample mean of the hyperspectral image data, η is the threshold for abnormal target detection and the test allows a decision to be made between two hypothesis tests, where RX (Y) < η then H when a decision is made 0 Hold, and no target hypothesis exists, when an abnormal target existsThen H 1 The assumption is true;
s5: algorithm optimization: the classical RX algorithm is optimized by the expert, wherein a low rank matrix w= { W is used first when the optimization is performed 1 ,w 2 ,…,w N Building a background covariance matrix
Figure BDA0004076031300000291
The process employs equation (14) and equation (15), and the equation (14) is formulated as +.>
Figure BDA0004076031300000292
The formula of the equation (15) is +. >
Figure BDA0004076031300000293
Wherein N is the number of pixels, and equation (16) is obtained by calculation, wherein the equation (16) is expressed as +.>
Figure BDA0004076031300000294
And reconstructing the background in the anomaly detection by constructing a new background using the anomaly detection result of equation (16), selecting the first θ components, the background data to construct a covariance matrix by equations (14) and (15), and the anomaly detection to complete the anomaly detection result of obtaining a hyperspectral image by equation (16).
The method for detecting the hyperspectral image abnormal target in one of the first embodiment, the second embodiment, the third embodiment and the fourth embodiment is tested, and the following results are obtained:
Figure BDA0004076031300000295
the method for detecting the hyperspectral image abnormal target prepared by the first embodiment, the second embodiment, the third embodiment and the fourth embodiment has obviously improved abnormal target detection efficiency and abnormal target detection precision compared with the existing method, and the first embodiment is the best embodiment.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.

Claims (9)

1. A method of detecting a hyperspectral image anomaly target, comprising the steps of:
s1: the method comprises the following steps: combining the representation-based method with the statistics-based method by a practitioner;
s2: the algorithm is obtained: obtaining a low-rank sparse decomposition hyperspectral anomaly detection algorithm based on clustering subspace accumulation by a professional;
s3: the acquisition method comprises the following steps: acquiring an unsupervised learning method of K-means clustering by a professional;
s4: non-stationary signal processing: processing the non-stationary signal by a fractional Fourier transform method;
s5: and (3) constructing a model: constructing a low-rank sparse matrix decomposition model by professionals;
s6: algorithm optimization: the classical RX algorithm is optimized by a professional.
2. The method for detecting abnormal targets of hyperspectral images according to claim 1, wherein in S1, a representation-based method and a statistics-based method are combined by a professional, and abnormal targets are detected by respective advantages of the methods, wherein hyperspectral images are clustered into several subspaces by using a k-means clustering method, and hyperspectral images are processed by using a fractional fourier transform and a low rank and sparse matrix decomposition method, while abnormality detection is performed in each subspace by using a modified RX detection method, and detection results of each subspace are accumulated, and final abnormality detection results are obtained by accumulation.
3. The method for detecting an abnormal object of a hyperspectral image according to claim 1 wherein in S2, the abnormal object is obtained by a professional based onA clustering subspace accumulated low-rank sparse decomposition hyperspectral anomaly detection algorithm, wherein the algorithm is input by original hyperspectral image data,
Figure FDA0004076031280000011
initialization CL, num, pr, r, k,
Figure FDA0004076031280000021
Γ，W，S
the steps are as follows:
1) The original hyperspectral image Y passes through the formula (3) to obtain a clustering subspace
Figure FDA0004076031280000022
2) Obtained in each subspace by using a fractional Fourier transform algorithm
Figure FDA0004076031280000023
3) At the position of
Figure FDA0004076031280000024
In (2), { W) is obtained by using Godec algorithm 1 ,W 2 ,…W i ,…,W ε }
4)
Figure FDA0004076031280000025
5) In each subspace, an abnormality detection result { Θ ] is obtained by the equation (16) 1 ,Θ 2 ,…Θ i ,…Θ ε }
6) Finally, the final abnormality detection result is obtained
Figure FDA0004076031280000026
And outputting a hyperspectral image anomaly detection result graph.
4. The method for detecting abnormal targets of hyperspectral images according to claim 1, wherein in S3, a professional obtains an unsupervised learning method of K-means clustering, wherein the unsupervised learning method of K-means clustering is an iterative clustering algorithm and a data clustering technology, and the data is divided into a specific number of clusters by the unsupervised learning method of K-means clustering, and is processed by the professional by the unsupervised learning method of K-means clustering.
5. The method of detecting a hyperspectral image anomaly target as claimed in claim 4 wherein the processing step is performed by (A) assuming a hyperspectral image matrix
Figure FDA0004076031280000027
Epsilon is the number of clusters, and the cluster center is assumed to be c= { C 1 ,c 2 ,c 3 ,…c j ,…c ε And Y is normalized, (B) randomly selecting B samples from the hyperspectral image dataset Y as initial cluster centers, (C) Y i (i=1, 2, … B; j=1, 2, … epsilon) is a sample in the hyperspectral image dataset and will be calculated from y i The distance to the cluster center is expressed as:
Figure FDA0004076031280000031
where L is the dimension of the sample, (D) find the minimum distance according to the calculated distance from each sample to the cluster center and divide the samples into corresponding clusters, (E) recalculate and update the cluster center according to equation (2) and calculate the result of the objective function according to equation (3) while judging the cluster center and the objective function, wherein the algorithm ends if the requirement is met and continues to step (B) if the requirement is not met, wherein the equation (2) is formulated as
Figure FDA0004076031280000032
(2) Equation (3) is
Figure FDA0004076031280000033
6. The method for detecting an abnormal object of a hyperspectral image according to claim 1 wherein in S4, the nonstationary signal is processed by fractional fourier transform, wherein the processing is performed assuming a hyperspectral image matrix
Figure FDA0004076031280000034
N is the number of pixels, kappa is the number of spectral bands, described by the process, where for each pixel y i It is described in the fractional fourier transform domain using equations (4), (5) and (6), and the equation (4) is formulated as +.>
Figure FDA0004076031280000035
The equation (5) is
Figure FDA0004076031280000041
The equation (6) is
Figure FDA00040760312800000410
Wherein->
Figure FDA0004076031280000042
And λ is an index, n is an integer, +.>
Figure FDA00040760312800000415
Is the fractional order of the fractional Fourier transform, and +.>
Figure FDA00040760312800000411
There is +.>
Figure FDA0004076031280000043
Figure FDA00040760312800000412
There is +.>
Figure FDA0004076031280000044
Said->
Figure FDA00040760312800000413
Is a rotation angle, and->
Figure FDA00040760312800000414
7. The method for detecting abnormal objects of hyperspectral image according to claim 1, wherein in S5, a low-rank sparse matrix decomposition model is constructed by a practitioner, wherein hyperspectral image matrix data is decomposed by the practitioner in low-rank and sparse matrix
Figure FDA0004076031280000045
Modeling is performed by using equation (7), wherein the equation (7) is expressed as y=w+s+e, wherein W represents the background of the hyperspectral image and is a low-rank matrix, S represents an abnormal target in the hyperspectral image of the sparse matrix, E is a noise matrix in the hyperspectral image, and the low-rank and sparse components are calculated by using a GoDec algorithm through the constructed model, wherein the calculation is performed by using equation (8), and the equation (8) is expressed as>
Figure FDA0004076031280000046
Where r and k are the upper bound of the rank and radix S of matrix W, +. >
Figure FDA0004076031280000047
Is the Frobenius specification and optimizes the problem (8) by solving two sub-problems alternately using equation (9), where equation (9) is formulated as +.>
Figure FDA0004076031280000048
And by singular values W t Threshold updating Y-S t-1 Wherein the singular value W t The calculation is performed by using the equation (10), wherein the equation (10) is as follows
Figure FDA0004076031280000049
At the same time through equation (11) threshold Y-L t Updating S t Wherein the formula of the formula (11) is +.>
Figure FDA0004076031280000051
And Ω represents the first |Y-W t Non-zero subset k of i, and P Ω (. Cndot.) represents the projection of the matrix onto the set Ω.
8. The method for detecting a hyperspectral image anomaly target as claimed in claim 7 wherein the GoDec algorithm content is (a) input:
Figure FDA0004076031280000052
hyperspectral image data matrix
r- - -maximum rank of hyperspectral image background
k-hyperspectral image sparse matrix cardinality
Figure FDA0004076031280000053
Error tolerance
Γ - -maximum number of iterations
(b) Initialization r=r 0 ，k＝k 0 ，
Figure FDA0004076031280000054
Γ＝Γ 0 ，W 0 ＝Y，
S 0 ＝sparse(zeros(size(Y)))，t:＝0
(c) When (when)
Figure FDA0004076031280000055
Execution of
t:＝t+1
(d) Updating variable W t First, assume M 1 ＝randn(P,r),
T 1 ＝Y-S t-1 ，X 1 ＝T 1 M 1 ，Z＝[T 1 T 1 T ]ΓT 1 ，Ψ 1 ＝ZM 1 ，
M 2 ＝Ψ 1 ，Ψ 2 ＝Z T Ψ 1 ，Ψ 1 ＝ZΨ 2
If rank (M) 2 Ψ 1 )<r has
Figure FDA0004076031280000057
Returning to step (c);
ending the program;
Figure FDA0004076031280000058
(e) Updating variable S t ,S t ＝P Ω (Y-W t )
(f) Output W, low rank component of hyperspectral image data
S, sparse component of hyperspectral image data, and obtaining RX detector method by improvement, wherein anomaly detection is performed by detecting result based on GoDec algorithm and processing low rank components W and S with RX detector, and in classical RX detectors 8,9, binary hypothesis of RX algorithm is defined as equation (12), equation (12) is that
Figure FDA0004076031280000061
Wherein H is 0 A=0, H when established 1 A > 0 when established, and B= [ B ] 1 ,b 2 ,…,b J ] T Is the spectral feature of the anomaly target, β is the vector representing the background noise, and the two hypothesis tests have the same background covariance and different mean values, by assuming the target feature B and the background covariance +.>
Figure FDA0004076031280000062
Unknown, where H 0 Hyperspectral data are +.>
Figure FDA0004076031280000063
H 1 Hyperspectral data are +.>
Figure FDA0004076031280000064
RX applies a threshold to detect the Markov distance between the test pixel and its background, and assuming it satisfies the multivariate normal distribution 8, equation (13) is obtained as +.>
Figure FDA0004076031280000065
Wherein->
Figure FDA0004076031280000066
Is the background covariance matrix of the hyperspectral image data,/>
Figure FDA0004076031280000067
Is the sample mean of the hyperspectral image data, η is the threshold for abnormal target detection and the test allows a decision to be made between two hypothesis tests, where RX (Y) < η then H when a decision is made 0 Hold, and if there is no target hypothesis, H is the case when there is an abnormal target 1 The assumption holds.
9. The method for detecting abnormal objects in hyperspectral image according to claim 1 wherein in S6, the classical RX algorithm is optimized by a professional, wherein the optimization is performed using a low rank matrix w= { W 1 ,w 2 ,…,w N Building a background covariance matrix
Figure FDA0004076031280000068
The process employs equation (14) and equation (15), and the equation (14) is formulated as
Figure FDA0004076031280000069
The formula of the equation (15) is +.>
Figure FDA00040760312800000610
Wherein N is the number of pixels, and equation (16) is obtained by calculation, wherein the equation (16) is expressed as +.>
Figure FDA0004076031280000071
And reconstructing the background in the anomaly detection by constructing a new background using the anomaly detection result of equation (16), selecting the first θ components, the background data to construct a covariance matrix by equations (14) and (15), and the anomaly detection to complete the anomaly detection result of obtaining a hyperspectral image by equation (16). />
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN116662794B (en) * 2023-08-02 2023-11-10 成都凯天电子股份有限公司 Vibration anomaly monitoring method considering data distribution update

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